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The gamma-ray sky >100 MeV is dominated by the diffuse emissions frominteractions of cosmic rays with the interstellar gas and radiation fields ofthe Milky Way. Observations of these diffuse emissions provide a tool to studycosmic-ray origin and propagation, and the interstellar medium. We presentmeasurements from the first 21 months of the Fermi-LAT mission and compare withmodels of the diffuse gamma-ray emission generated using the GALPROP code. Themodels are fitted to cosmic-ray data and incorporate astrophysical input forthe distribution of cosmic-ray sources, interstellar gas and radiation fields.To assess uncertainties associated with the astrophysical input, a grid ofmodels is created by varying within observational limits the distribution ofcosmic-ray sources, the size of the cosmic-ray confinement volume (halo), andthe distribution of interstellar gas. An all-sky maximum-likelihood fit is usedto determine the Xco-factor, the ratio between integrated CO-line intensity andmolecular hydrogen column density, the fluxes and spectra of the gamma-raypoint sources from the first Fermi-LAT catalogue, and the intensity andspectrum of the isotropic background including residual cosmic rays that weremisclassified as gamma rays, all of which have some dependency on the assumeddiffuse emission model. The models are compared on the basis of their maximumlikelihood ratios as well as spectra, longitude, and latitude profiles. We alsoprovide residual maps for the data following subtraction of the diffuseemission models. The models are consistent with the data at high andintermediate latitudes but under-predict the data in the inner Galaxy forenergies above a few GeV. Possible explanations for this discrepancy arediscussed, including the contribution by undetected point source populationsand spectral variations of cosmic rays throughout the Galaxy. [Abridged]

Fermi-LAT Observations of the Diffuse Gamma-Ray Emission: Implications for Cosmic Rays and the Interstellar Medium